I just tried to set up Chiaki on mxlinux and ran into issues rebinding the controls to my dual sense. I am running the appimage or the most recent Chiaki and was able to connect to my PS5. When trying to rebind the controls from KB it was not recognizing any inputs from my controller. I made sure I had libsdl up to date and checked a few games on steam and the controller seems to be working there. I found a workaround using a program to bind your controller buttons to key input, but that seems like a bad way to go about it limiting the sticks and triggers to only on/off.
Would it be easier to just use wine or lutris to run the standard PS remote program?
If Steam can recognize the input from the controller, but the other program cannot, it means the OS is getting the input, and this Chiaki program either doesn't have permissions to read the input, or it's looking in the wrong place. I'm not seeing much documentation for it unfortunately, but you can try starting it from a terminal to try and get some debug output when it runs and see if it's throwing any errors.